Although economists do believe that price ceilings are a bad idea, it is not really because demand will force the price above the ceiling. If the ceiling is properly administered, prices will not (at least officially) go above the ceiling.

Instead, it is typically said that there will be three major factors that will make the price ceiling counterproductive.

First, a black market might spring up. In this black market, the price will go above the ceiling that is set because there will be many buyers willing to pay more. So, in that sense, your statement is correct, though an illegal market must be set up in order to allow the price to go above the ceiling.

Second, sellers may allow the quality of their goods to deteriorate. For example, if a landlord cannot charge enough rent to make a profit, he or she may stop maintaining the buildings as well as they otherwise would have. This causes the good to be worth less than it is supposed to be.

Finally, suppliers may simply abandon the market. They may decide that they cannot make a good enough profit under the price ceiling and stop selling altogether.

In all of these ways, price ceilings are said to be counterproductive. So, your statement is generally true, but there is much more to the argument than the idea that the price will exceed the ceiling.

If the government has set a price ceiling, prices cannot go above it unless there is no monitoring of the price by the government to ensure that it is always below the price ceiling that has been set.

When a price ceiling is set, producers are not able to increase prices when the demand rises; this usually results in a decrease in supply and a shortage of the good in the market. But this is the case in perfect competition and price ceilings are not meant to be used here.

Government intervention is not pointless in many cases. For example, consider the case of a life-saving medicine. A company that has devoted a considerable amount of its resources in developing the medicine is not likely to stop manufacturing it unless the variable costs exceed the total price. It would not make any sense for the company to stop production and get no returns for the investments already made unless by doing so it can force the government to raise the price ceiling or have it removed entirely.

The price ceiling though will prove to be a disincentive for development of new medicines as there is no guarantee that the company will get the required returns.

A price ceiling can be used to regulate a monopoly but it requires a lot of information to be able to arrive at a price that allows the monopolist to make sufficient profits for it to continue operations but keep the price in a range that consumers can afford.

A price ceiling is unrealistic unless the government intends to be heavily involved in regulating the market. An example is the price of milk. There is usually no real advantage to the government regulating the price that closely, except in unusual circumstances.